This is a carryover from when printing presses used actual plates. The initial edition would carry all numbers from 1 to whatever. When the second edition would be printed, the printer would simply erase the last number (the 1) from the plate, indicating that the lowest number was the current printing run.
I used to work in a small town press and the local paper would employ the same idea for its editions. The first run, which I would deliver to the stores, was the two-star edition. After the first batch was done, the printer would go to the platen, erase one of the stars, and start the press run for the snail mail edition that would ship later to the customers who received copies by mail.
(edit: whoops, failed to read OP...but leaving here for the small press newspaper reference. Printers are interesting cats. You shall know them by their missing digits. No, not the numbers in the editionsm but the missing fingers lost between the rolling plates.)
The edition number is always explicit, because for a new edition the pages are re-set. For a new printing the pages are (traditionally) not re-set, which is why the printing number has to be encoded in some manually-updatable way.
Can anyone confirm/deny Grouse's comment from the article?
"It's unlikely that a single set of metal plates would survive multiple printings. They wear out pretty fast. Instead, this would be used on the film negative used to expose the photosensitive plates. Of course, now people are printing directly to the plates instead, skipping the film step."
http://blogs.msdn.com/b/oldnewthing/archive/2007/04/10/20657...
For xerographic (and other chemical process) prints, what you say is probably true. For relief printing (think Gutenberg), this convention seems reasonable, though you'd have to grind, not scratch, away the extra number. I don't know enough book history to say whether this convention is old enough to have started from relief printing, but that's the only way it makes sense to me.
You can normally tell via other clues. For example, the design of the cover, a first edition may say that the book has been nominated for an award, whereas later editions will mention winning the award, an adaption to film, the film's awards etc. Another example might be the material used and colour of the hardback's cover. Even spelling mistakes.
The numbers aren't always reliable though... publishers can reprint multiple times and keep them as the same edition number. So, if you do want to purchase an early edition then do research on the book beforehand.
I used to work in a small town press and the local paper would employ the same idea for its editions. The first run, which I would deliver to the stores, was the two-star edition. After the first batch was done, the printer would go to the platen, erase one of the stars, and start the press run for the snail mail edition that would ship later to the customers who received copies by mail.
(edit: whoops, failed to read OP...but leaving here for the small press newspaper reference. Printers are interesting cats. You shall know them by their missing digits. No, not the numbers in the editionsm but the missing fingers lost between the rolling plates.)